The invention is related to the field for measuring the mechanical properties of materials, and more specifically to a technique for measuring the elastic modulus and hardness of the thin film in a film-on-substrate system using depth-sensing indentation techniques, also known as nanoindentation.
Nanoindentation techniques have been widely used for measuring the mechanical properties of solids in various forms at small scale. In a typical indentation test, a diamond tip is driven into the specimen surface under controlled load, and the displacement of the indenter tip is continuously monitored with high resolution sensors. Various mechanical properties (most typically the elastic modulus and hardness) of the indented material can be measured by analyzing the indentation data, without the necessity of imaging the indent. Since 1992, the method proposed by Oliver and Pharr has been established as a standard procedure for analyzing indentations performed on monolithic materials, and is generally referred to as the Oliver-Pharr method [1].
Oliver-Pharr method was intended for monolithic solids. The procedure becomes problematic when applied on a film-on-substrate system, where the substrate can be mechanically different from the film material. Significant error can be induced on the estimation of the contact area between the indenter and the specimen, thus affecting the measurement accuracy of the film properties. This is because the indenter detects not only the response of the film, but also that from the substrate. In general, the error due to the substrate effect increases with increasing indentation depth and with increasing elastic mismatch between film and substrate. To minimize the effect of the substrate on the measurement, the indentation depth is often limited to less than 10% of the film thickness. This empirical rule is not always reliable, especially if the elastic mismatch between film and substrate is large. It is also not useful for ultra-thin films when experimental issues make it difficult to obtain reliable measurement from shallow indentations. Evidently there exists a need for a method that can be used to analyze thin-film indentation data for indentation depths where the substrate effect cannot be ignored.
Oliver-Pharr method is based on Sneddon's elastic solution of indenting an elastic half space with a rigid punch. The contact area is estimated by assuming that the contact periphery behaves as described by the elastic solution. Sneddon's solution dictates that the sink-in depth in an elastic indentation is:
                              h          s                =                  ɛ          ⁢                      P            S                                              (        1        )            where ε is a constant depending on the punch geometry (e.g. ε=0.72 for conical tip), P is the indentation load, and S is the contact stiffness between the tip and the specimen. S is measured in an unloading process from the peak load since the recovery of material during unloading is mainly elastic. S can also be continuously measured throughout the entire indentation test by imposing a relatively small oscillatory force at high frequency onto the quasi-static load [1, 2].
The sink-in depth is then used to obtain the contact depth according tohc=h−hs  (2)The contact area is calculated from contact depth using the area function of the indenter tip:Ac=f(hc)  (3)The area function ƒ(hc) describes the cross-section area of the indenter as a function of the distance to its tip and is known a priori. For a conical tip, the contact radius is as follows:
                    a        =                                                            A                c                            π                                =                                    h              c                        ·                          tan              ⁡                              (                θ                )                                                                        (        4        )            The reduced indentation modulus Er is calculated from the contact stiffness S and contact area Ac as follows:
                              E          r                =                                            π                        2                    ⁢                      S                                          A                c                                                                        (        5        )            The reduced modulus is related with the elastic constants of the sample as follows:
                              1                      E            r                          =                                            1              -                              υ                2                                      E                    +                                    1              -                              υ                tip                2                                                    E              tip                                                          (        6        )            where E and υ is the Young's modulus and Poisson's ratio of the sample, respectively, and Etip and υtip is the same quantities for the indenter material (usually diamond).
For a film-on-substrate system, however, EQ 1 and 5 are no longer valid, and hs in general is not equal to
  ɛ  ⁢            P      S        .  Thus, the invention provides a method for measuring the elastic modulus and hardness in film-on-substrate system.